Correlational analysis, Basics, Assumptions for Pearson, Spearman Tests
1 like614 views
The document discusses correlation analysis, including definitions, types of correlation (positive, negative, and zero), and characteristics of the correlation coefficient. It explains the coefficient of determination, the impact of data transformations on correlation, and clarifies the distinction between correlation and causation. Additionally, it covers methods of calculating correlations and testing statistical assumptions using various correlation methods.
Correlational analysis, Basics, Assumptions for Pearson, Spearman Tests
- 1. Correlational Analysis A. Michael J Leo, PhD Assistant Professor of Education St. Xavier’s College of Education (Autonomous) Palayamkottai – 627 002 Tirunelveli, India 9994006762 amjlsxce@gmail.com
- 2. Correlation • The Degree of Relationship between the paired scores • The extend of the variations of one Variable going with the variations of the other. • It is the standardized Value of Co-variance 2 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 3. Curvilinear Relationship Example : Energy Usage Vs. Outside Temperature 3 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 4. Covariance Vs. Correlation 4 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 5. TYPES Positive Correlation Negative Correlation Zero Correlation (Non-Sense Correlation) 5 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 6. Characteristics of Correlation Co-efficient 6 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 7. 1. Range of Co-efficient of Correlation Weak +Ve Correlation -1 Perfect Negative Correlation +1 Perfect Positive Correlation Moderate +Ve Correlation Strong/High +Ve Correlation Strong/High -Ve Correlation Moderate -Ve Correlation -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Weak –Ve Correlation Zero Correlation 7 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 8. Positive Correlation 22 22 21 21 20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 CC=+1 8 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 9. Negative Correlation 22 13 21 14 20 15 19 16 18 17 17 18 16 19 15 20 14 21 13 22 CC=-1 9 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 10. Towards Zero Correlation (Non-Sense Correlation) 20 19 19 14 13 13 17 11 16 20 15 12 14 17 13 18 12 16 11 15 CC=0.074 10 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 11. 2. The Co-efficient of Determination, R2 • If r=0.6, then r2 = 0.36 (36%) • It means 36% of the variance in Y scores has been accounted for by the variance in X Scores. 11 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 12. • The undermined proportion of Y is called by k2 known as Co-efficient of non-determination. • k2 = 1- r2 • So k= √1-r2 Where k= co-efficient of alienation which is refereed as the degree of the lack of relationship. 12 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 13. 3. The effect of Origin and Unit • If every score in either or both distribution is increased or multiplied by a constant , the correlation co-efficient does not change. • If you measure in any unit, the co-efficient will not be affected . 13 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 14. 4. Correlation Co-efficient and Causation • Correlation co-efficient does not represent the causation • It may be a chain of relationship among the variables. • Causation can be inferred by conducting controlled experiments • Causation always ensures Correlation 14 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 15. 5. The Extreme values affects the Correlation coefficient. 6. The sampling Error and Errors of Measurement. 7. The size of the sample will affect the correlation coefficient 15 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 16. Methods of Calculation : Correlation Co-efficient 16 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 17. The Product Moment Correlation: The Assumptions (Karl Pearson) (a) The distribution of the two variables is bivariate normal (b) There is homoscedasticity (c) The residuals are independent (d) Both Variables represent either Ratio/Interval Data 17 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 18. The Product Moment Correlation: Applications (a) Describing a relationship between two variables as a descriptive statistic (b)Examining a relationship between two variables in a population as an inferential statistic (c) Providing various reliability estimates such as Cronbach's alpha, test-retest reliability, and split-half reliability (d)Evaluating validity evidence (e)Gauging the strength of effect for an intervention program. 18 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 19. Appropriate Method X Y Product Moment Correlation Interval/Ratio Interval/Ratio Spearman's Correlation/ Kendall's tau Ordinal/ Transformed Order Ordinal/Transformed Order Point-Biserial Correlation Interval/Ratio Nominal (Dichotomous ) Ex: Male/Female (Natural) Biserial Correlation Interval/Ratio Dichotomous (Artificial) Ex: Pass/Fail ( Continuous and Normal) Tetra-choric Correlation Dichotomous (Artificial) Ex: Pass/Fail ( Continuous and Normal) Dichotomous (Artificial) Ex: Pass/Fail ( Continuous and Normal) Phi-Coefficient Nominal Nominal 19 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 20. Appropriate Method Conditions Multiple Correlation Correlation among more than two variables. When the need for Multiple Regression arises Partial Correlation Partial correlation is the correlation between two variables with the effect of (an)other variable(s) held constant. Canonical Correlation A list of Variables (indicators) to Explain any One Concept (X) A list of Variables (indicators) to Explain any One Concept (Y) Intra-class Correlation Degree of agreement among judges Interval/Ratio Cohen's Kappa Degree of agreement among judges In the Form of Contingency Table 20 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 21. SPSS: Testing the Assumptions (Product Moment Correlation) • Scales need to be Continuous • The Raw score could be used for the test • Check the Outliers • Check the normality • Check the liner Linear Relationship • Check the Homoscedasticity 21 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 22. The Assumptions (Spearman Rank Correlation) • Fix the scale as Ordinal/Likert • Check the Monotonic Relationship • Use Raw data or transformed rank data 22 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 23. Kendal Tau • It has Inquisitive Interpretation • Better Estimation of population parameter • For small sample, it is accurate • It is good, when there is tie over the ranks 23 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil
- 24. Thank You 24 A. Michael J Leo, PhD, Assistant Professor, St. Xavier's College of Education, Palayamkottai - 627002, Tirunelveli, Tamil